4GS Scientijic Intelligence. [June, 



occasionally oliserved tlicm ? If so, are small stars distingiiishable 

 in such situations ? or is it only when a star of the fiist or second 

 magnitude happens to pass near the zenith that sueii a phenomenon 

 is perceived ? 



Is it a fact, as hns Ijeen related hy some authors, that the cele- 

 brated astronomer Tycho Brahe had an observatory in a deep pit or 

 dungeon, where he frequently sat and contemplated the stars in the 

 day-time, as refiected from mirrors which were placed around him 

 in (liflrrent positions for this purpose ? 



An answer to any of the al)ove queries, if they be not deemed too 

 unimportant for discussion in the Annaii of Philosophy, will much 

 oblige, Sir, yours, &c. T. Dick. 



Meihven, near Perth, April, 1815. 



IX. On the Explanation of the Fluclionary Calcuhis. 



(To Dr. Thomson.) 

 SIR, 



The following ideas owe tiieir origin to the valuable article of 

 Professor Christison in your last number. Their merit is certainly 

 only of the ordinary kind, yet their publication may perhaps do 

 some good. 



To facilitate the conception of the generation of fluxional quan- 

 tities, I conceive that if the line A D (see the Professor's figure) be 

 considered as a cylinder, on which is rolled a sheet of paper, 

 divided into the two parallelograms, A F, C E, tiie former being 

 coloured black, and tlie latter red ; then, when the paper is un- 

 rolled, it will be easy for the student to comprehend the generation 

 of the rectangles, and also their constant ratio to each other, which 

 (Euclid i. 6,) is as A E to E D, or, in the Professor's example, as 

 5 to I. 



Again, if A C D E, in fig. 2, represent a piece of paper forming 

 a parallelogram, as A D, and a triangle, as A B C, having a series 

 of equidistant lines, as N M L, H G F, &e. &c. drawn parallel to 

 C B D, and on which the res]>ective proportions of C B to B D, of 

 N M to M L, of H G to G F, &c. &c. are written, then if CD 

 represent a cylinder on which the paper is rolled, commencing at 

 C D, it is manifest when the paper is unrolled that A E will be the 

 part first visible, and as it continues to be unfolded, the generation 

 of the |jarallelogram and triangle, and also the ratio of their rates 

 of increase, by the numbers on tlie parallel lines, at any instant or 

 position, will be shown in the easiist and most familiar manner. 



This simple contrivance will, I conceive, illustrate completely 

 the Professor's idea, as tlie generation of the quantities can be easier 

 comprehended by this mode than by supposing them to be produced 

 by the motion of a line. I perfectly agree with your learned Cor- 

 respondent, that the first principles of this science, and indeed 

 somewhat more, may he attained hy very young persons; and it is 

 .singular tliat a simple and elementary treatise adjipted to their com- 



